Stochastic analysis is often understood as the analysis of functionals defined on the Wiener space, i.e., the space on which the Wiener process is realized. Since the Wiener space is infinite-dimensional, it requires a special calculus, the so-called Malliavin calculus.

This book provides readers with a concise introduction to stochastic analysis, in particular, to the Malliavin calculus. It contains a detailed description of all the technical tools necessary to describe the theory, such as the Wiener process, the Ornstein-Uhlenbeck process, and Sobolev spaces. It also presents applications of stochastic calculus to the study of stochastic differential equations. The volume is suitable for graduate students and research mathematicians interested in probability and random processes.